# How do you simplify (2sqrt(5x))/sqrt(25x^2)?

Mar 29, 2017

See the solution process below:

#### Explanation:

We can rewrite this expression as:

$\frac{2 \sqrt{5 x}}{\sqrt{5 x} \sqrt{5 x}}$

We can next cancel common terms in the numerator and denominator:

$\frac{2 \textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{5 x}}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{5 x}}} \sqrt{5 x}}} \implies$

$\frac{2}{\sqrt{5 x}}$

Now we can rationalize the denominator by multiplying the fraction by the appropriate form of 1:

$\frac{\sqrt{5 x}}{\sqrt{5 x}} \times \frac{2}{\sqrt{5 x}} \implies$

$\frac{\sqrt{5 x} \times 2}{\sqrt{5 x} \times \sqrt{5 x}} \implies$

$\frac{2 \sqrt{5 x}}{5 x}$